I interpret that as, the whistle after injury is so THEY can resume playing, whereas with a drop ball WE are already restarting the game by the dropping of the ball thus negating the need for whistle.
That has always been my interpretation too. There is absolutely nothing that we do that says play is restarted that is clearer than giving the players the ball. Make sure they are paying attention obviously and that any carnage has been cleared from the pitch, but why on earth do the players next to you need to hear your whistle to know you will are ready to give them the ball back?
I'll eat humble pie if the IFAB and DE say it's the other way.